Question

A spherical conductor with a 0.193 m radius is initially uncharged. How many electrons should be removed from the sphere in order for it to have an electrical potential of 7.10 kV at the surface?

Answer 1

Answer:

The number of electrons removed is  $N = 9.513 *10^{11}$

Explanation:

From hr question we are told that

    The radius is  $r = 0.193 \ m$

   The required electrical potential is $V = 7.10 \ kV = 7.10 *10^{3} V$

The total charge on the sphere  is mathematically evaluated as

           $Q = \frac{Vr}{k}$

where k is the coulombs constant with value $k =9)*10^{9} \ kg\cdot m^3\cdot s^{-4}\cdot A^2.$

substituting value

          $Q = \frac{7.10 *10^3 * 0.193}{9*10^9}$

          $Q = 1.522*10^{-7} C$

The number of electron removed is mathematically evaluated as

        $N = \frac{Q}{e}$

Where e is  the charge on one electron with value $e = 1.6 *10^{-19} \ C$

  substituting values  

      $N = \frac{1.522 *10^{-7}}{1.60*10^{-19}}$

      $N = 9.513 *10^{11}$